Active control of two orthogonal polarizations for heterodyne beam delivery

ABSTRACT

A polarization control system includes a beam source that generates a first beam component containing light with a first polarization and a first frequency and a second beam component containing light with a second polarization and a second frequency. A polarization state modulator adjusts the polarizations of the components for transmission on a single optical fiber. A detector system measures polarizations of the components when output from the optical fiber and determines how to adjust the polarization state modulator in order to give the first and the second components the desired output polarization states. The beam source can be implemented using a Zeeman-split laser, a laser containing a birefringent element, a pair of phase-locked lasers, and/or a variety of configurations of electro-optic or acousto-optic crystals operated to create or enhance the frequency difference between the beam components.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent document is a divisional and claims the priority of U.S.patent application Ser. No. 10/728,559, filed Dec. 5, 2003, now U.S.Pat. No. 6,961,130 which is a continuation-in-part of U.S. patentapplication Ser. No. 10/439,970, filed May 15, 2003, now U.S. Pat. No.6,961,129 both of which are hereby incorporated by reference in theirentirety.

BACKGROUND

Measurement optics in a polarization based or multiplexed heterodyneinterferometer such as used for precision measurements in semiconductordevice manufacturing equipment generally require a light beam includingorthogonal polarization components that have slightly differentfrequencies. However, the light sources such as lasers that generate therequired beams also produce heat and temperature gradients that aregenerally unacceptable for precision operation of the interferometermeasurement optics. Accordingly, the light sources generally must beseparated from the measurement optics. Transmission of the polarizationcomponents on a single optical fiber is generally not used because evena polarization-maintaining (PM) fiber will typically change thepolarizations too much for the precise measurements.

In one system for beam delivery, a beam splitter feeds one polarizationcomponent to a first PM fiber and feeds the second polarizationcomponent to a second PM fiber. The two separate fibers carry the twocomponent beams to the interferometer optics near the measurement site.Polarizers, alignment optics, and a combiner can then recombine the twocomponent beams so that the beams travel along a common path. Suitablealignment optics include, for example, collimators, flat transmissivewindows, polarizing optics, beam splitters, and total and partialreflectors to translate and tilt the beams. The interferometer opticsthen reflect one of the component beams off of a stage being measuredand reflect the other component off of a reference reflector. The phasedifference between the two beams after respective reflections indicatesthe displacement or movement of the stage.

Conventional interferometer systems using two PM fibers for beamdelivery often require sensitive alignment processes for the optics andcombiner that recombine the two component beams. Additionally, havingtwo fiber paths generally requires duplication of equipment or opticalelements, which can increase system cost and size. Thus, a system thatmaintains the polarization of two light beams in a single fiber couldreduce cost and complexity.

SUMMARY

In one embodiment of the invention, a polarization control systemincludes a beam source that generates two beam components withorthogonal polarizations and different frequencies. A polarization statemodulator adjusts the polarization states of the two beam components fortransmission on a single optical fiber. At the output from the fiber, adetector measures the output polarizations of the components. One suchdetector includes three detector paths that generate a first beatsignal, a second signal, and a third signal from the two light beams. Anamplitude detector determines the amplitude of the first beat signal ata beat frequency. A phase comparator determines the phase differencebetween the second and third signals. The system then uses the amplitudeand the phase difference to determine how to adjust the polarizationstate modulator in order to give the first and the second light beamsthe desired polarizations when output from the fiber.

The beam source can be implemented using a Zeeman-split laser, a lasercontaining a birefringent element, a pair of phase-locked lasers, and/ora variety of configurations of electro-optic or acousto-optic crystalsthat are operated to create or enhance the frequency difference betweenthe beam components.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a polarization control system in one embodiment ofthe invention for maintaining the polarized states of twoorthogonally-polarized light beams.

FIGS. 2 and 3 are flowcharts of methods for operating the polarizationcontrol system of FIG. 1.

FIG. 4 illustrates a polarization control system in one embodiment ofthe invention for maintaining the polarization states of two orthogonallinearly-polarized light beams.

FIG. 5 illustrates a polarization state modulator in the polarizationcontrol system of FIG. 4.

FIGS. 6A, 6B, 6C, and 6D illustrate polarization control systems formaintaining the polarization states of two orthogonal linearly-polarizedlight beams in embodiments of the invention.

FIG. 7 illustrates a non-remote configuration of a polarization controlsystem in one embodiment of the invention.

FIG. 8 illustrates a polarization control system using dithering tomaintain the polarized states of two orthogonal light beams in oneembodiment of the invention.

FIG. 9 illustrates a system in accordance with an embodiment of theinvention employing a Zeeman-split laser and active control ofpolarizations output from an optical fiber.

FIG. 10 shows a Zeeman-split laser with cavity elements for control andstabilization of frequency difference and polarization.

FIGS. 11A and 11B illustrate alternative embodiments of lasers usingbirefringent materials in laser cavities to create a frequencydifference between polarization components.

FIGS. 12A and 12B illustrate polarization control systems in accordancewith embodiments of the invention that use phase-locked lasers.

FIG. 13 illustrates a polarization control system in accordance with anembodiment of the invention in which a beam source uses an electro-opticmodulator in generating a heterodyne beam.

FIGS. 14A, 14B, and 14C illustrate beam sources incorporating a varietyof different configurations for use of acousto-optic modulators onseparated polarization components.

FIG. 15 illustrates a beam source using a dual frequency acoustic wavein an acousto-optic crystal to produce a frequency difference betweendiverging diffracted beams.

FIGS. 16A, 16B, and 16C illustrate beam sources that convert divergingbeams having the same polarization into orthogonally-polarized beams.

FIGS. 17A, 17B, 17C, 17D, and 17E illustrate beam sources employingdiffracted and non-diffracted beams from acousto-optic crystals withalternative configurations.

FIG. 18 illustrates a beam source using an acousto-optic crystal havingseparate interaction regions through which acoustic waves propagate.

DETAILED DESCRIPTION

In accordance with an aspect of the invention, a beam delivery systemfor a heterodyne interferometer uses a single fiber for delivery of aheterodyne beam containing frequency components with orthogonal linearpolarizations. To deliver frequency components having the requiredorientations, the beam delivery system measures the magnitude and phaseof a beat frequency in a polarization component and actively adjusts thepolarizations of the beams input to the fiber to minimize the magnitudeof the beat signal.

FIG. 1 illustrates a polarization control system 10 in one embodiment ofthe invention. System 10 is implemented in a remote operationconfiguration where a polarization state modulator 14 is locatedupstream from an optical fiber 16 that feeds an interferometer system.

A polarization state modulator (PSM) generally converts an inputpolarization state into an output polarization state. One or moreexternal inputs applied to the PSM controls the polarization conversion,and in general, the output polarization state differs from the inputpolarization state. For example, PSM 14 may consist of multiple variableretarders. A retarder (or waveplate) is an optical device that resolvesa light wave into two orthogonal polarization components and produces aphase shift (or retardance) between them. The resulting light wave isgenerally of a different polarization form. Ideally, retarders simplychange the polarization form of a light beam without polarizing orinducing an intensity change in the light beam. A variable retarder hasa retardance that can be changed by external means, e.g., by theapplication of a voltage.

In system 10, a beam source 12 generates (1) a light beam E1 with apolarization state P1 and a frequency ω1 and (2) a light E2 with apolarization state P2 and a frequency ω2. In one embodiment, beam source12 includes a Helium Neon (HeNe) laser and electro-optical componentsrequired to generate the desired polarizations and frequencies. Forexample, beam source 12 can be a 5517D laser made by AgilentTechnologies. PSM 14 receives light beams E1 and E2 and adjusts initialpolarization states P1 and P2 to polarization states P1′ and P2′,respectively, before launching light beams E1 and E2 into fiber 16. PSM14 is operable to change any input polarization state P1 or P2 to anydesired output polarization state P1′ or P2′. In one embodiment, PSM 14includes a voltage-controlled variable retarder 18 oriented at 0°, avoltage-controlled variable retarder 20 oriented at 45°, and avoltage-controlled variable retarder 22 oriented at 0°. Voltages V1, V2,and V3 control respective retarders 18, 20, and 22 to generaterespective retardances Γ1, Γ2, and Γ3.

Fiber 16 carries light beams E1 and E2 downstream to interferometeroptics at a measurement site. In one embodiment, fiber 16 is apolarization-maintaining (PM) fiber. Experiments show that fiber 16changes the polarization states P1′ and P2′ of light beams E1 and E2 topolarization states P1″ and P2″, respectively, that generally depend onthe temperature and mechanical deformation of fiber 16. Nonetheless,fiber 16 produces negligible change to the orthogonal relationshipbetween the polarization states of light beams E1 and E2.

At the measurement site, a beam splitter 24 divides light beams E1 andE2 into two paths. An output path 26 carries light beams E1 and E2 tothe distance-measuring interferometer (hereafter “DMI”) system. Amonitor path 28 carries a fraction of the power from light beams E1 andE2 to components that monitor the polarization states P1″ and P2″ ofbeams E1 and E2 as described hereafter. Some or all of the componentsalong the monitor path 28 can be located either at the measurement siteor away from the measurement site. For example, light exiting components38, 52, and 62 can be coupled to respective multimode fibers inconjunction with focusing lenses leading to the detector components awayfrom the measurement site.

A beam splitter 30 splits light beams E1 and E2 on monitor path 28 intotwo paths. A path 32 carries light beams E1 and E2 to a first detectorpath 34, and a path 36 carries light beams E1 and E2 to other detectorpaths. First detector path 34 includes a polarizer 38 that allows thecomponents of light beams E1 and E2 at a selected polarization state P3to reach a light detector 40. A focusing lens may be interposed betweenpolarizer 38 and light detector 40 to focus the light. In response tothe light intensity received, light detector 40 transmits a beat signalB1 at a beat frequency of (ω1–ω2) to an amplitude-sensing device 42.Beat signal B1′ represents the optical power detected at beat frequency(ω1–ω2). An amplifier may be interposed between light detector 40 andamplitude-sensing device 42 to amplify beat signal B1. Before polarizer38, first detector path 34 can optionally include one or more waveplates 37. Wave plates 37 and polarizer 38 are selected according to thedesired orientation of the output polarization states of light beams E1and E2. In particular, wave plates 37 and polarizer 38 can be selectedso that beat signal B1 is small (ideally zero) when polarizations P1″and P2″ are along the desired directions.

A beam splitter 44 receives light beams E1 and E2 from path 36 anddivides them into two paths. A path 46 carries light beams E1 and E2 toa second detector path 48, and a path 50 carries light beams E1 and E2to another detector path. Second detector path 48 includes a polarizer52 that allows the components of light beams E1 and E2 at a selectedpolarization state P4 to reach a light detector 54. A focusing lens maybe interposed between polarizer 52 and light detector 54. In response tothe light intensity received, light detector 54 transmits a beat signalB2 to a phase detector 56. An amplifier may be interposed between lightdetector 54 and phase detector 56. Before polarizer 52, second detectorpath 48 optionally includes one or more wave plates 51. Wave plates 51and polarizer 52 are selected to generate a large beat signal B2depending on the desired orientation of the output polarization statesof light beams E1 and E2.

Path 50 carries light beams E1 and E2 to a third detector path 58. Thirddetector path 58 includes a polarizer 62 that allows the components oflight beams E1 and E2 at a selected polarization state P5 to reach alight detector 64. A focusing lens may be interposed between polarizer62 and light detector 64. In response to the light intensity received,light detector 64 transmits a beat signal B3 to phase detector 56. Anamplifier may be interposed between light detector 64 and phase detector56. Before polarizer 62, the third detector path 58 optionally includesone or more wave plates 60. Wave plates 60 and polarizer 62 are selectedto generate a beat signal B3 that has a different phase relationshipwith beat signal B2 for each of the two possible solutions of E1 and E2corresponding to a minimum amplitude detected by amplitude-sensingdevice 42 in first detector path 34. In one embodiment, the phaserelationship is 90° out of phase (i.e., beat signals B2 and B3 are inquadrature) when beams E1 and E2 have the desired polarizations.

Phase detector 56 determines a phase difference ΔΨ between beat signalsB2 and B3. Amplitude-sensing device 42 determines an amplitude B1′ ofbeat signal B1 at the beat tone frequency (i.e., ω1–ω2). A controller 43uses amplitude B1′ and phase difference ΔΨ to generate control voltagesor signals V₁, V₂, and V₃ that are applied to PSM 14 in order to achievethe desired polarization states P1″ and P2″ of light beams E1 and E2.Amplifiers may be interposed between controller 43 and PSM 14 to amplifythe control signals V₁, V₂, and V₃. Controller 43 can be implementedusing analog or digital components.

Specifically, controller 43 adjusts PSM 14 until beat tone amplitude B1′reaches one of two local minimums. Beat tone amplitude B1′ has two localminimums, one minimum corresponding to linear polarizations P1″ and P2″having the desired orientations, and the other minimum corresponding tolinear polarizations P1″ and P2″ being rotated by 90°. Controller 43uses phase difference ΔΨ to uniquely determine the polarization statesof E1 and E2 because the phase difference ΔΨ has different values at thetwo minimums that correspond to the two orientations of E1 and E2. Theexact correspondence between the values of phase difference ΔΨ and theorientations of E1 and E2 can be derived conventionally using Jonescalculus.

FIG. 2 illustrates one embodiment of a method 100 for using system 10 tolock into a desired polarization orientation. In a step 104, controller43 performs a global search for an initial solution of retardances Γ1,Γ2, and Γ3 that would produce a local minimum with the correctpolarization orientation. The values of Γ1, Γ2, and Γ3 in the initialsolution are used as the initial retardance values. One embodiment ofstep 104 is described later in reference to FIG. 3.

In steps 106 to 114, controller 43 adjusts retardance Γ1 of retarder 18to find the minimum value of beat tone amplitude B1′ that can beachieved with retardance Γ1. Specifically, in step 106, controller 43selects retarder 18. In step 108, controller 43 increments retardance Γ1by adjusting voltage V1. In step 110, controller 43 determines if beattone amplitude B1′ has decreased. If so, step 110 is followed by step108. Otherwise, step 110 is followed by step 112.

In step 112, controller 43 decrements retardance Γ1 by adjusting voltageV1. In step 114, controller 43 determines if beat tone amplitude B1′ hasdecreased. If so, step 114 is followed by step 112. Otherwise, step 114is followed by step 116.

In steps 116 to 124, controller 43 adjusts retardance Γ2 of retarder 20to find the minimum value of beat tone amplitude B1′ that can beachieved with retardance Γ2. Step 124 is followed by step 126 once theminimum value of beat tone amplitude B1′ has been achieved. In steps 126to 134, controller 43 adjusts retardance Γ3 of retarder 22 to find theminimum value of beat tone amplitude B1′ that can be achieved withretardance Γ3. Step 134 is followed by step 136 once the minimum valueof beat tone amplitude B1′ has been achieved.

In step 136, controller 43 records the value of beat tone amplitude B1′for the current iteration. In step 138, controller 43 determines phasedifference ΔΨ between beat signals B2 and B3. In step 140, controller 43determines if the value of phase difference ΔΨ corresponds to thedesired output polarization states of E1 and E2. Phase difference ΔΨ maynot correspond to the desired output polarization states if there is alarge and sudden change in the condition of fiber 16 that causes a largeand sudden change in the polarization states of beams E1 and E2, whichmay cause the control loop to lose lock momentarily, and hence thesystem may not be locked to the same initial solution thereafter. If so,then step 140 is followed by step 104 where method 100 is repeated tosearch for another initial solution of retardances Γ1, Γ2, and Γ3. Ifphase difference ΔΨ corresponds to the desired output polarizationstates of E1 and E2, then step 140 is followed by step 142.

In step 142, controller 43 determines if the current beat tone amplitudeB1′ is the same as the beat tone amplitude B1′ recorded from theprevious iteration. If so, then step 142 is followed by 136 and method100 loops until the beat tone amplitude B1′ changes value. If thecurrent beat tone amplitude B1′ is not the same as the beat toneamplitude B1′ recorded from the previous iteration, then step 142 isfollowed by step 106, and method 100 is repeated to search for anotherminimum beat tone amplitude B1′.

FIG. 3 illustrates one embodiment of step 104 where controller 43searches through some or all of the polarization states of E1 and E2 foran initial solution of retardances Γ1, Γ2, and Γ3 that produces thedesired orientation of the polarization states of beams E1 and E2. Instep 174, controller 43 initializes retardances Γ1, Γ2, and Γ3 to 0.Minimum values of zero retardance are assumed here, but the search canstart from any minimum value of retardances Γ1, Γ2, and Γ3 achievable bythe retarders or desired to be searched. In step 176, controller 43records phase difference ΔΨ between beat signals B2 and B3 generatedwith the current values of retardances Γ1, Γ2, and Γ3. In step 178,controller 43 determines if retardance Γ3 exceeds its maximum value. Themaximum value may be the maximum retardance desired to be searched orthat a retarder can achieve. If retardance Γ3 exceeds its maximum value,then step 178 is followed by step 182. If retardance Γ3 has not exceededits maximum value, then step 178 is followed by step 180. In step 180,controller 43 increments retardance Γ3 by adjusting voltage V3. Step 180is followed by step 176 and the above steps loop until retardance Γ3exceeds its maximum value.

In step 182, controller 43 reinitializes Γ3 to 0. In step 184,controller 43 increments retardance Γ2 by adjusting voltage V2. In step186, controller 43 determines if retardance Γ2 exceeds its maximumvalue. If so, then step 186 is followed by step 188. If retardance Γ2has not exceeded its maximum value, then step 186 is followed by step176 and the above steps loop until both retardances Γ3 and Γ2 exceedtheir maximum values.

In step 188, controller 43 reinitializes Γ2 to 0. In step 190,controller 43 increments retardance Γ1 by adjusting voltage V1. In step192, controller 43 determines if retardance Γ1 exceeds its maximumvalue. If so, then step 192 is followed by step 194. If retardance Γ1has not exceeded its maximum value, then step 192 is followed by step176 and the above steps loop until retardances Γ3, Γ2, and Γ1 exceedtheir maximum values. In step 194, controller 43 selects the values ofretardances Γ3, Γ2, and Γ1 that produce a desired phase difference ΔΨ₀,which corresponds to the desired output polarization states of componentbeams E1 and E2, as the initial solution for method 100.

FIG. 4 illustrates one implementation of system 10 in FIG. 1, hereaftersystem 10A, which is applicable to a specific orientation of thepolarization states in one embodiment of the invention. In system 10A,light beam E1 from beam source 12 initially has a vertical linearpolarization (VLP) P1, and light beam E2 initially has a horizontallinear polarization (HLP) P2. In system 10A, the polarization states P1″and P2″ of light beams E1 and E2 at the output of fiber 16 should be thesame as polarization states P1 and P2, respectively. In this embodiment,polarizer 38 is oriented at 90°, polarizer 52 is oriented at 45°, waveplate 60 is a quarter-wave plate oriented at 45°, and polarizer 62 isoriented at 90°.

FIG. 5 illustrates one embodiment of a PSM 14A used to adjust thepolarization states of component beams E1 and E2 in system 10A (FIG. 4).PSM 14A is a rotatable variable retarder made of an electro-opticcrystal, such as a lithium niobate crystal (LiNbO₃), with lightpropagation in the z-direction and voltages applied in the x andy-directions. The polarization axes and retardance of the LiNbO₃ arecontrolled by changing voltages V_(x) and V_(y) so that any inputpolarization state can be transformed into any output polarization stateif both V_(x) and V_(y) operate over a range [−V_(π), V_(π)], where thehalf-wave voltage V_(π) is λd/(2n₀ ³r₂₂L), λ is the wavelength of thelight beam, d is the width and height of the block of LiNbO₃, n₀ is theordinary index of the LiNbO₃, and r₂₂ is the electro-optical coefficientof the LiNbO₃.

In one embodiment, system 10A can use a method similar to method 100(FIGS. 2 and 3) to maintain the desired polarization states of componentbeams E1 and E2. Controller 43 first performs a global search to findinitial values of voltages V_(x) and V_(y) that produce a desired phasedifference ΔΨ₀. Controller 43 then performs a minimum searchcontinuously to lock onto the minimum corresponding to the desired phasedifference ΔΨ₀.

When a PM fiber is used in the systems described above, component beamsE1 and E2 typically undergo a small polarization change (e.g., less than20% power change through the polarizer). Thus, there may not be a needfor a PSM that can generate all the possible input polarization statesin order to find and lock to the desired output polarization states. Infact, a proper design can reduce the range of polarization states thatneeds to be searched, thereby allowing the elimination of some variableretarders and possibly the quadrature detection. For example, onlypolarization states covering half of the Poincare sphere (a mathematicalconstruction which describes all polarization states) may need to besearched.

FIG. 6A illustrates one implementation of system 10 in FIG. 1, hereaftersystem 10B, which is applicable to small changes in the polarizationstates in one embodiment of the invention. In system 10B, beam source 12generates a VLP beam E1 and a HLP beam E2. System 10B then maintains thepolarization states of component beams E1 and E2 at the output of fiber16.

A retarder 252 and a PSM 14B are used to produce a subset of thepossible polarization states of component beams E1 and E2. Retarder 252is a half-wave plate oriented at 22.5°. PSM 14B includes (1) a variableretarder 254 oriented at 0° and having a variable retardance that rangesfrom 0 to λ/2, and (2) a variable retarder 256 oriented at 45° andhaving a variable retardance that ranges from 0 to λ/2. Retarder 252 andPSM 14B allow approximately half of the Poincare sphere to be searchedso system 10B will lock onto only one of the two minimums of beat toneamplitude B1′, since the design excludes the other solution.Furthermore, retarder 252 and PSM 14B allow polarization states to bescanned continuously without any breaks within the region of interest(e.g., half the Poincare sphere) that would otherwise require one ormore additional variable retarders to provide endless (i.e., reset-free)polarization control.

System 10B includes only one detector path, i.e., the first detectorpath 34 that generates beat signal B1. Controller 43 uses only beatsignal B1 to lock onto the only minimum within the input polarizationstates that PSM 14B can produce. No global search for an initialsolution is needed, as only one minimum is accessible within the inputpolarization states that retarder plate 252 and PSM 14B can produce. Asearch for the initial solution in half of the Poincare sphere is stillrequired.

FIG. 6B illustrates a system 10C that is similar to system 10B but usesa different retarder and a different PSM. In particular, system 10C usesa quarter-wave plate 262 oriented at −45° and PSM 14A (FIG. 5). Asdescribed above, PSM 14A is a rotatable variable retarder controlled byvoltages V_(x) and V_(y), wherein voltage V_(x) operates over a range[0, V_(π)] and voltage V_(y) operates over a range [−V_(π), V_(π)].Retarder 262 and PSM 14A allow approximately half of the Poincare sphereto be searched continuously without any breaks in the polarizationstates that would otherwise require one or more additional rotatablevariable retarders to provide endless polarization control.

While the desired polarization states for a heterodyne interferometertypically correspond to a VLP beam E1 and a HLP beam E2, it is possibleto design a system that locks component beams E1 and E2 to polarizationstates other than VLP and HLP while still obtaining VLP and HLP statesbefore E1 and E2 enter the interferometer. FIG. 6C illustrates such asystem 10D in one embodiment of the invention. System 10D is similar tosystems 10B and 10C except for modifications described below. The inputpolarization states are a VLP beam E1 and a HLP beam E2. System 10D usesneither retarder 252 (FIG. 6A) nor retarder 262 (FIG. 6B). PSM 14Dincludes (1) a variable retarder 254D oriented at 45° and operating overa retardance range of 0 to λ/2, and (2) a variable retarder 256Doriented at 0° and operating over a retardance range of λ/2 to 3λ/2. Aquarter-wave plate 600 oriented at 45° is included in detector path 34before polarizer 38 so that the minimum beat amplitude corresponds to aleft circular polarization (LCP) state of beam E1 and a right circularpolarization (RCP) state of beam E2. A second quarter-wave plate 602oriented at 45° is included in path 26 to convert the LCP beam E1 andRCP beam E2 to a VLP beam E1 and a HLP beam E2 before they enter theinterferometer.

FIG. 6D illustrates a system 10E, which combines the features of system10B and system 10D, in one embodiment of the invention. In system 10E,beam source 12 generates component beams E1 and E2 with polarizationstates depending on the application. Similar to system 10B, a retarder252E and a PSM 14E can produce a subset of the possible polarizationstates of component beams E1 and E2. The retardance and the orientationof retarder 252E depend on the input polarization states and the desiredoutput polarization states of E1 and E2. Similar to system 10D, aretarder 600E is included in detector path 34 before polarizer 38 sothat the minimum beat amplitude corresponds to the desired polarizationstates of E1 and E2. A retarder 602E is included in path 26 to convertcomponent beams E1 and E2 to the desired polarization states beforecomponent beams E1 and E2 enter the interferometer. Again, theretardance and the orientation of retarder 602E depend on the desiredpolarization states of beams E1 and E2.

The various embodiments of the polarization control system describedabove have all been shown in a remote operation configuration, where thePSM is located upstream from the fiber and the measurement site. FIG. 7illustrates an embodiment of a non-remote polarization control system300 where a PSM 314 is located downstream from a fiber 316 near themeasurement site. As can be seen, a light source 312 launches two lightbeams with orthogonal polarization states and different frequencies intofiber 316. Fiber 316 then carries the two light beams to PSM 314. PSM314 adjusts the polarization states of the two light beams beforesending them to an output path and a monitor path. PSM 314 can beimplemented using similar principles as those discussed in conjunctionwith FIGS. 1, 4, 5, 6A and 6B. The output path leads to interferometeroptics. The monitor path leads to a detection and control block 334 thatgenerates the feedback control to PSM 314 to maintain the desired outputpolarization states of the two light beams. Block 334 can be implementedin a similar way as those described above with reference to FIGS. 1, 4,6A, and 6B.

FIG. 8 illustrates another implementation of system 10 in FIG. 1,hereinafter system 10F, which locks onto the desired beat tone amplitudeB1′ using dithering. The technique of dithering generates smallmodulation terms to each control signal in order to aid the detection ofthe derivative of the detected signal (including sign). This techniquealso filters out changes in amplitude detected by amplitude-sensingdevice 42 due to other factors such as mechanical vibration andtemperature variation. System 10F is similar to system 10 butadditionally includes signal generators 402, 404, and 406 and adders408, 410, and 412. Signal generators 402, 404, and 406 generate smallorthogonal modulation signals s1, s2, and s3 (which could be sinusoidalat frequencies f1, f2, and f3). Controller 43 detects signals s1, s2,and s3 and generates three signals 414, 416, and 418 using correlationtechniques, which are added to corresponding control dither signals s1,s2, and s3 to generate control signals V₁, V₂, and V₃ to variableretarders 18, 20, and 22, respectively.

Various other adaptations and combinations of features of theembodiments disclosed are within the scope of the invention. Forexample, the desired output polarization states do not need to be thesame as the input polarization states emerging from the light source.One embodiment of system 10B in FIG. 6A can be used for inputpolarization states corresponding to a left circularly-polarized beam E1and a right circularly-polarized beam E2 from the laser, and forgenerating desired output polarization states corresponding to a VLPbeam E1 and a HLP beam E2. In such an embodiment, retarder 252 would bea quarter-wave plate oriented at 90°. Similarly, one embodiment ofsystem 10C in FIG. 6B can be used for input polarization statescorresponding to a left circularly-polarized beam E1 and a rightcircularly-polarized beam E2 from the laser, and for generating desiredoutput polarization states corresponding to a VLP E1 and a HLP E2. Insuch an embodiment, retarder 262 would not be needed.

Various alternative embodiments of the PSM can be used in theembodiments described above. One embodiment of the PSM includes two ormore fiber squeezers whose birefringence properties are varied by theapplication of mechanical stresses. Mechanical stresses are applied tothe fiber squeezers in response to the control signals from controller43. Another embodiment of PSM includes two or more liquid crystal cellswhose retardances and/or polarization axes are varied in response to thecontrol signals from controller 43. Yet another embodiment of PSMincludes two or more mechanically rotatable wave plates with fixedretardance. The wave plates are rotated in response to the controlsignals from controller 43. Yet another embodiment of the PSM includestwo or more photoelastic modulators whose linear birefringence areinduced by the application of mechanical stresses. Mechanical stressesare applied to these photoelastic modulators in response to the controlsignals from controller 43.

Various alternative embodiments of the beam source that provide theinitial heterodyne light beam can also be employed. FIG. 9 illustratesan exemplary embodiment of the invention in which a beam source 12Aincludes a Zeeman-split laser 502 such as in the 5517D laser mentionedabove. In Zeeman-split laser 502, an axial magnetic field applied to theresonant cavity in the laser produces a beam with two orthogonalcircularly-polarized components that have different frequencies. Opticalsystem 504, which preferably includes a quarter-wave plate, converts theorthogonal circularly-polarized components into orthogonallinearly-polarized component beams E1 and E2 suitable for polarizationcontrol as described above.

An optical system 505 including one or more waveplates converts the twoorthogonal polarizations from beam source 12A into two appropriateorthogonal polarization states. The orthogonal polarization stateschosen depend on the exact configuration of the PSM, such as those shownin FIGS. 6A to 6D. The waveplates in system 505 may be combined withwaveplate 504 depending on construction of beam source 12A. Otherembodiments discussed below may also include a similar optical system505 having the function as described here. This description however, isnot repeated in each of the following embodiments.

Beam source 12A transmits the dual-frequency or heterodyne beam throughPSM 14 and a polarization maintaining optical fiber 16 to beam splitter24 and through beam splitter 24 to a path 26 to further interferometeroptics. As described above, the PSM can either precede the fiber asshown in FIG. 9 or follow the fiber as shown in FIG. 7. Beam splitter 24also directs a fraction of the heterodyne beam into a polarizationmonitoring system 70. Monitoring system 70, which generally determineswhether the output beam from the transmission system including opticalfiber 16 and PSM 14 has the desired polarization components, can beimplemented using a beat signal amplitude detector with or without aphase detector as described above. Based on the measurements ofmonitoring system 70, controller 43 sets the control signals for PSM 14as required to ultimately result in the output beam components E1″ andE2″ having the desired polarizations P1″ and P2″.

Depending on the configuration of PSM 14, birefringence waveplates maybe included after splitter 24 if necessary to convert the two orthogonalpolarization components in beam 26 to vertical and horizontal linearpolarization components. More generally, similar elements that providefixed changes of the orthogonal polarizations can be provided in any ofthe disclosed embodiments of the invention, even where the discussion ofsuch elements is not be repeated.

FIG. 10 illustrates a specific embodiment of an actively stabilizedZeeman-split laser 12B similar to a laser disclosed in U.S. Pat. No.5,586,133, which is hereby incorporated by reference in its entirety.Zeeman-split laser 12B includes a tube 510 containing electrodes 520 and522 that can be driven (e.g., with an RF signal) to cause a populationinversion in a laser gain medium 524. An output coupler mirror 528 and areflector 518 are at the ends of tube 510, and define the length of theresonant cavity.

A permanent magnet 526 produces an axial magnetic field along thedirection of a light beam 530 oscillating between output coupler mirror528 and reflector 518. The axial magnetic field has two effects on lasergain medium 524. The applied magnetic field causes the Zeeman effect,which splits gain curve of medium 524 into two gain curves, one for leftcircularly-polarized light and the other for right circularly-polarizedlight. Additionally, the Faraday effect splits the real part ofrefractive index curve into two curves, one for leftcircularly-polarized light and the other for right circularly-polarizedlight. As a result, the output beam 530 transmitted through outputcoupler mirror 528 has a left circularly-polarized component with awavelength that differs from the wavelength of the rightcircularly-polarized component of light beam 530. An optical element 534such as a quarter-wave plate can transform the orthogonalcircularly-polarized components of beam 530 into orthogonal linearcomponents.

Zeeman-split laser 12B further uses an adjustable magneto-opticalapparatus in and around tube 510 to increase the split frequencydifference between the two polarizations. The magneto-optical apparatusincludes an optically transparent medium 512 in the path of beam 530 intube 510, a permanent magnet 514 that is outside of enclosure 510 andsurrounding optically transparent medium 512, and an electromagnet 516surrounding permanent magnet 514. Permanent magnet 514 and electromagnet516 produce a magnetic field of adjustable magnitude along the directionof laser beam 530. Since the Faraday effect is many orders of magnitudestronger in optically transparent medium 512 than in laser gain medium524, the magnitude of frequency split introduced by the opticallytransparent medium can be much larger than that of the laser gainmedium. In addition to increasing the frequency split, the opticallytransparent medium also permits active stabilization of the frequencydifference between the polarization components.

To stabilize the absolute frequencies and the difference frequency ofthe polarization components of beam 530, a beam splitter 532 reflects aportion of beam 530 to a detector 540. In the illustrated embodiment,detector 540 detects the frequency difference between the two orthogonalpolarization components of beam 530 and detects at least one of thecomponent frequencies. If a detected frequency differs from the desiredfrequency, a drive circuit 542 adjusts cavity length of tube 510 (e.g.,by setting the power to a heating element 536 causing tube 510 to expandor contract) as required to adjust the output frequency. Detector 540also generates an electrical signal having the difference or beatfrequency for the polarization components of beam 530. Feedback controlcircuit 546 compares the signal from detector 540 to the frequency of anelectronic oscillator 544 and actively adjusts the current throughelectromagnet 516 to set the magnetic field in medium 512 to a strengththat provides the desired frequency difference.

Including a birefringent material in a laser cavity is another methodfor generating a heterodyne beam as described in U.S. Pat. No.5,091,912, which is hereby incorporated by reference in its entirety.FIG. 11A schematically shows a laser 12C including a birefringent block558 and other laser gain medium 560 in a resonant cavity 550 having alength defined by the separation of mirrors 552 and 554. In a well-knownarrangement, one mirror 554 can be flat while the other mirror 552 isspherically concave and centered on mirror 554. Laser 12C also includeselectrodes or other means (not shown) for causing lasing, e.g., forcausing gas discharge using an RF current. An aperture 556 placed closeto concave mirror 552 can select the fundamental transverse mode of beam570 in resonant cavity 550.

As shown in FIG. 11A, the positions of aperture 556, birefringent block558, and other components of laser 12C are such that two orthogonallinear polarization components defined by the optical axes ofbirefringent block 558 have separate paths 572 and 574 of differentoptical lengths, causing resonant cavity 550 to have two resonant modes.A first plate 562, which is a quarter-wave for the mean frequency of thetwo modes, is in close proximity to birefringent block 558, on the sideof block 558 where the ordinary beam and the extraordinary beam followthe same path. The neutral lines of quarter-wave plate 562 are at 45°from the polarization axes of birefringent block 558, so as to balancethe light intensities of the two modes excited in the lasing cavity 510.A second quarter-wave plate 564, also placed in the common path of thetwo beams, is more remote from block 558 than is plate 562. Angularadjustment of plate 564 about the direction of the light beams canadjust the difference between the frequencies of the two resonant modes.

The frequency difference can be changed by angular adjustment of plate564. Accordingly, a feedback control system similar to the one discussedin paragraph in regard to FIG. 10 can stabilize the frequency differencebetween the two polarization components from laser 12C. In this case,the feedback controller adjusts the angle of plate 564 to change thefrequency difference.

FIG. 11A illustrates an embodiment of laser 12C where output throughmirror 552 provides collinear output of both frequency/polarizationcomponents. Alternatively, output through mirror 554 would provideseparate beams having differing frequencies and polarizations.

FIG. 11B shows a laser 12D having a configuration using two birefringentblocks 558 and 568. Components of laser 12D are arranged so that a zoneof cavity 550 in which the inherent oscillation states are separatedspatially is away from both mirrors 552 and 566, which may consequentlybe concave mirrors. In particular, birefringent blocks 558 and 568,which may be substantially identical, are positioned in cavity 550 sothat the propagation paths of the two polarization states merge outsidea zone straddling active lasing medium 560. Laser 12D thus formed mayhave a better immunity to deformation of cavity 550.

Another technique for producing a heterodyne beam containingpolarization components with different frequencies uses a pair ofphase-locked lasers. FIG. 12A shows a system including a beam source 12Econtaining two lasers 602 and 604. Laser 602, which can be afrequency-stabilized laser, directs a beam having a first frequency f1into a reflector or a polarizing beam splitter (PBS) 606. PBS orreflector 606 reflects a polarization component of the input beam to asecond PBS 608 that is transparent to that polarization component. PBS608 also receives a beam having a frequency f2 from laser 604 andreflects a polarization component that is orthogonal to the transmittedpolarization component from PBS 606. A resulting combined beam 610 fromPBS 608 includes orthogonal polarization components that have respectivefrequencies f1 and f2.

Accurate control of the frequency difference f2−f1 can be maintainedusing active feedback. In particular, beam source 12E includes a beamsplitter 612 that reflects a portion of beam 610 through a polarizer 614into a detector 616. With polarizer 614 having an axis that is at 45°with the polarizations of the frequency components of beam 610, detector616 can generate an electrical signal having the beat frequency f2−f1 ofthe two frequency components. A phase-lock circuit 618 compares thefrequency of the signal from detector 616 to an electronic referencefrequency from an oscillator 620 and generates a control signal thatsets the output frequency f2 of laser 604. For example, phase lockcircuit 618 can control the power provided to a heating element or otherdevice that controls the length of the resonant cavity in laser 604. Inthis manner, the frequency difference f2−f1 can be tightly controlled asrequired for precision interferometer measurements.

FIG. 12B illustrates a beam source 12F according to an embodiment usingcoupled Zeeman-split lasers 622 and 624 to generate a heterodyne beamwith the desired properties. Laser 622 produces a beam with left andright circularly-polarized components having frequencies f1 and f2′. Aquarter-wave plate 626 between laser 622 and PBS 606 converts orthogonalcircularly-polarized components into vertical and horizontallinearly-polarized components such that PBS 606 reflects only lighthaving frequency f1. Similarly, laser 624 produces a beam with left andright circularly-polarized components having frequencies f1′ and f2, anda quarter-wave plate 628 between laser 624 and PBS 608 convertsorthogonal circularly-polarized components into vertical and horizontallinearly-polarized components such that PBS 608 reflects only lighthaving frequency f2. In an embodiment where PBS 606 and 608 areidentical, a half-wave plate 607 can be included between PBS 606 and 608so that the polarization component reflected in PBS 606 is transmittedthrough PBS 608. Detector 616 as described above can measure a portionof the combined output beam from PBS 608 to permit phase lock circuit618 to control laser 624 as required to maintain a desired frequencydifference f2−f1.

The output beam from beam source 12E or 12F can thus be used with apolarization control system including a PSM 14, an optical fiber 16, abeam monitor 70, and a controller 43 having the functions describedabove. Alternatively, the functions of beam monitor 70 and detector 616can be integrated into a single system that measures the properties ofthe output beam and actively controls both PSM 14 and the coupled lightsources to ensure that the heterodyne beam used for interferometermeasurements has the desired frequencies and polarizations. U.S. Pat.No. 6,052,186 further describes beam sources including dual lasersystems and is hereby incorporated by reference in its entirety.

Another way to generate a heterodyne beam for an interferometer is touse an electro-optic modulator on the output beam from a laser. FIG. 13shows an example of a beam source 12G that uses an electro-opticmodulator 632 to split the frequencies of orthogonalcircularly-polarized components output from a laser 630. The laser 630can be a monochromatic laser or a Zeeman-split laser, and electro-opticmodulator 632 can be made of a material such as lithium niobate. Themodulator can be configured to act as a rotating half-wave plate thatcreates a frequency shift between the left and right circularpolarization components. Since the modulator creates a frequency shiftbetween the left and right circular polarization components, laser 630must produce both left and right circular components (at the same ordifferent frequencies), preferably with similar optical powers. One ormore waveplates may be included between the laser 630 and modulator 632to convert polarization states of the beam from laser 630 into left andright circular polarizations. The following presumes a modulator made oflithium niobate crystal, although other materials may be used. In orderfor the modulator to act as a rotating half-wave plate, an amplifiedelectrical oscillator 634 applies a first AC voltage of the form V_(π)sin(2πf_(a)t) to electro-optic modulator 632 to create a correspondingelectric field component in the X-direction perpendicular to thepropagation of the beam, and another amplified oscillator 636 applies asecond AC voltage of the form V_(π) cos(2πf_(a)t) to create acorresponding electric field component in the Y-direction perpendicularto the propagation of the beam, where V_(π) is the half-wave voltage andf_(a) is the drive frequency. The out-of-phase applied voltages V_(π)sin(2πf_(a)t) and V_(π) cos(2πf_(a)t) cause electro-optic modulator 632to act as a half-wave plate having an axis rotating at an angular rateof 7πf_(a) radians per second. As a result, modulator 632 creates afrequency difference of 2f_(a) between left and rightcircularly-polarized components of the beam traversing modulator 632. Anoptical element such as a quarter-wave plate 638 can convert theorthogonal circular polarizations into orthogonal linear polarizationsuitable for a polarization control system including PSM 14, opticalfiber 16, monitor 70, and controller 43.

Acousto-optic modulators (AOMs) can also be used to create or increasethe frequency difference between polarization components. U.S. Pat. No.5,485,272, for example, describes several heterodyne beam sourcesemploying AOMs and is hereby incorporated by reference in its entirety.An example of an AOM is an acousto-optic Bragg cell (e.g., a uniaxialbirefringent crystal) with an attached electro-acoustic transducer. Theelectro-acoustic transducer converts the electrical signal into soundwaves that the transducer launches through the birefringent crystal. Inone embodiment, the birefringent crystal can be oriented such that soundwaves propagate along the optic axis of the crystal. The sound wavesformed in the material generate refractive index variations in thematerial, resulting in a three-dimensional diffraction grating known asa Bragg grating. This grating diffracts a beam traversing the modulatorinto a plurality of diffraction orders.

In order to concentrate as much radiation as possible in one diffractedorder, Bragg's condition should be met for that particular order. Forexample, in the case of maximizing diffracted power into the firstorder, the condition sin θ_(d)=λf_(a)/(2V_(a)) should be met, whereθ_(d) is the angle which the input beam makes with the Bragg gratinglines, f_(a) is the acoustic frequency, λ is the optical wavelength ofthe input beam, and V_(a) is acoustic velocity. As a result of Braggdiffraction, the output optical wave from the birefringent crystal issubject not only to diffraction but also to a frequency shift. Only theundiffracted order propagates through the crystal with no change inpropagation angle and optical frequency; all other diffracted ordersundergo a change in propagation angle as well as a shift in opticalfrequency depending on several parameters such as the diffracted order,the propagation direction of the acoustic wave relative to that of theinput beam, and the drive frequency. The text “Acousto-Optic Devices:Principles, Design, and Applications,” Jieping Xu & Robert Stroud, JohnWiley & Sons Inc., 1992 further describes the operation of AOMs.

FIGS. 14A to 14C illustrate some alternative embodiments for heterodynebeam sources using one or more AOM.

FIG. 14A illustrates a beam source 12I using a Zeeman laser 640 and apair of AOMs 642 and 652. A polarizing beam splitter 648 directs a first(e.g., vertical linear) polarization component and a second (e.g.,horizontal linear) polarization component into two separate paths. Theinput beam can then enter the crystals of AOMs 642 and 652 at the Braggangle for the first diffracted order. An oscillator 654 with amplifier656 drives AOM 652 to create a traveling acoustic wave that shifts thefrequency of the diffracted second polarization component. In thisembodiment, both AOM 642 and AOM 652 increase the frequencies of thefirst and second polarization components so that an added frequencydifference between the polarization components is equal to thedifference in the drive frequencies to AOM 642 and AOM 652,respectively, which is chosen to be non-zero. This configuration allowsgeneration of polarization components that have a frequency differencesubstantially smaller than each drive frequency to the AOM 642 or 652.

Since propagation direction of the diffracted beam is different fromthat of the input beam in general, alignment optics 643 and 653 are usedto adjust the propagation angle of the separate polarization componentsoutput from respective AOMs 642 and 652 so that they travel the requiredpaths for entering beam combiner 650. Beam combiner 650 recombines thepolarization components into a collinear beam suitable for transmissionon a single fiber 16 in a polarization monitoring system including PSM14, beam monitor 70, and controller 43.

FIG. 14B shows another configuration capable of generating a beam withpolarization components having a frequency difference substantiallysmaller than each drive frequency to the AOM. In FIG. 14B, a beam source12J includes a polarizing beam splitter 658 and a beam combiner 660implemented using birefringent material. Each element 658 or 660 may bea birefringent system such as a Wollaston prism, a Fresnel prism, aKoester prism, or a Rochon prism. Such birefringent systems may beseparate optical elements or integrated into the material of the AOMs642 or 652. Alternatively, instead of a birefringent element, othersystems such as a diffraction grating or a phase grating can be used forbeam splitting and/or combining.

Polarization optics 662 can be included immediately after Zeeman-splitlaser 640 if necessary so that light incident on PBS 658 is linearlypolarized at 45° to the polarization axis of PBS 658. As a result, thetwo polarization components exiting PBS 658 carry similar opticalpowers, which is generally preferred for heterodyne interferometerapplications, and have polarization directions 643 and 653,respectively, as shown in FIG. 14B. Polarization optics 662 can also bechosen to produce an arbitrary polarization state other than linearpolarization at 45° if different optical powers for the two beams aredesired. The separated beam components from PBS 658 traverse respectiveAOMs 642 and 652 having respective optical axes 641 and 651. PBS 658 isdesigned such that the two output beams enter each of the AOM 642 andAOM 652 respectively at the Bragg angle of the desired diffracted order.

AOMs 642 and 652 cause frequency shifts in the respective traversingbeams. The opposite drive directions to AOM 642 and 652 in FIG. 14Bresult in generation of a beam with two polarization components whosefrequency difference is given by the frequency difference of the twodrive frequencies. Alternatively, the frequency difference between thetwo polarizations can be made equal to the sum of the drive frequenciesif the drive directions are the same for AOM 642 and AOM 652; howeverthis configuration is generally less useful for heterodyneinterferometers.

FIG. 14C illustrates another beam source 12K in which beam splitter 658separates the polarization components but directs both polarizationcomponents sequentially through AOMs 664 and 666 having respective opticaxes 663 and 665. The separated polarization components travel inopposite directions through AOM 664. Accordingly, the sign of thefrequency shift that AOM 664 introduces is opposite for the twopolarization components. Diffraction of the separated polarizationcomponents in AOM 664 directs the polarization components into AOM 666,which again introduces opposite frequency shifts before beam combiner660 recombines the polarization components into a collinear beam. Asystem including a series of three or more AOMs can be similarlyconstructed. The resulting output beam from beam source 12K contains abeam with two polarization components whose frequencies differ by twotimes the difference between the drive frequencies applied to AOM 664and AOM 666, respectively. As a result, a beam with two orthogonallypolarized components that have a frequency difference substantiallysmaller than twice the acoustic frequency can be produced.

In another embodiment of beam source 12K, laser 640 can be aZeeman-split laser. Polarization optics 641 immediately following lasertransform left and right circular polarizations from the Zeeman-splitlaser 640 into two output beams with orthogonal linear polarizationshaving polarization direction aligned with the polarization axis of thepolarizing beam splitter 658. As a result, PBS 658 splits the two beams,each with a different frequency, into two orthogonally-polarized beams,which propagate through the AOMs 664 and 666, respectively. In thisembodiment, the two AOMs are used to increase the frequency splitbetween the two orthogonal components, which have an initial non-zerofrequency difference when emerging from Zeeman-split laser 640.Polarization beam splitter 660 then recombines the two beams to form asingle output beam with two orthogonal linear polarizations and anincreased frequency split.

FIG. 15 illustrates a beam source 12L including a source 670 of amonochromatic beam and an acousto-optic Bragg cell 672 using analternative technique for generating a heterodyne beam. In beam source12L, the single light beam 671 incident upon the acousto-optic Braggcell 672 preferably has a linear polarization oriented at 45° to theplane of the figure. An amplified oscillator 674 drives Bragg cell 672to generate traveling acoustic waves of two frequencies f_(a) and f_(b).Acousto-optic Bragg cell 672 diffracts the light beam from light source670 giving rise to a light beam 682 associated with the travelingacoustic wave of frequency f_(a) and a light beam 684 associated withthe traveling acoustic wave of frequency f_(b). Light beams 682 and 684,which generally have the same polarization as input beam 671, differ infrequency by about the frequency difference |f_(a)−f_(b)| and diverge ata small angle corresponding to the separation between the diffractionmaxima. The electrical output of power amplifier 674 can be adjusted sothat beams 684 and 682 carry approximately the same optical power.Source 670, acousto-optic Bragg cell 672, and oscillator 674 can thusform a source 680 of a divergent heterodyne beam.

Another optical system 676 converts the two frequency components havingthe same polarizations but different propagation directions into twoparallel beams having orthogonal linear polarizations. In an exemplaryembodiment, beams 684 and 682 after exiting Bragg cell 672 are incidenton a birefringent prism 676 that is made of a crystal (e.g. quartz) withthe optical axis parallel to the apex edge. An apex angle α ofbirefringent prism 676 satisfies Equation 1. In Equation 1, δ′ is theangle separation between beams 684 and 682, n_(o) and n_(e) are theordinary and extraordinary indices of refraction respectively, and θ isthe exit angle of the output beam 678 relative to the normal from theoutput surface of prism 676. Birefringent prism 676 acts on intermediatebeams 684 and 682 to split each into two orthogonally polarized beams,one parallel and one perpendicular to the plane of the figure, toproduce two output beams 682A and 684A and two spurious beams 682B and684B. Spurious beams 682B and 684B have directions of propagationdifferent from the output beams 682A and 684A and can be eliminated byaperture 678, or by a conventional pinhole spatial filter arrangement.Light sources similar to beam source 12L are further described in U.S.Pat. No. 4,684,828, which is hereby incorporated by reference in itsentirety.δ′=sin⁻¹ [n _(o) sin {α−sin⁻¹(sin θ/n _(o))}]−sin⁻¹ [n _(e) sin{α−sin⁻¹(sin θ/n _(e))}]  Equation 1:

FIG. 16A illustrates a beam source 12M including an alternative opticalsystem for converting beams 682 and 684 that have the same polarizationbut different frequencies and different propagation directions intoparallel beams 692 and 694. In this embodiment, beams 682 and 684 areincident on a phase retardation plate 686, typically made of abirefringent crystal. The directions of polarizations of incident beams682 and 684 are substantially at 45° to the plane of the figure, and theoptical axis 687 of phase retardation plate 686 is at an angle β withrespect to a normal to the entrance face of phase retardation plate 686.Upon entering the plate 686, beam 684 splits into internal beamcomponents 684Y and 684X, wherein internal beam components 684Y and 684Xare ordinarily and extraordinarily polarized, respectively. Similarly,beam 682 forms internal beam components 682Y and 682X, wherein internalbeam components 682Y and 682X are ordinarily and extraordinarilypolarized. Since beam components 684 and 682 are incident on theretardation plate at different angles relative to the optic axis 687,extraordinarily polarized beam components 684X and 682X propagate withinretardation plate 686 with phase velocities corresponding to differentindices of refraction.

In general, Equation 2 indicates the index of refraction for anextraordinarily polarized beam propagating at an angle θ with respect toan optic axis of a birefringent crystal. In Equation 2, n_(o) and n_(e)are the ordinary and extraordinary principal indices of refraction ofthe birefringent crystal. The different indices of refraction for beamcomponents 682X and 684Y can be determined from Equation 2. The index ofrefraction for ordinarily polarized beam components 682Y and 684Y isn_(o). According to these indices of refraction, the optic axis 687orientation and the thickness of retardation plate 686 are chosen suchthat retardation plate 686 introduces a phase shift of pπ radians inbeam 682X relative to beam 682Y and a phase shift of (p+1) π radians inbeam 684X relative to beam 684Y, p being an integer. Typically the angleβ is set at a value substantially equal to 45°.1/n ²=cos² θ/n _(o) ²+sin² θ/n _(e) ²  Equation 2:

Beams 682X, 682Y, 684X, and 684Y exit phase retardation plate 686 asbeams 682A, 682B, 684A, and 684B, respectively. As a consequence of thephase shifts introduced in beams 682X, 682Y, 684X, and 684Y, thepolarization of portions of beams 682A and 682B that overlap one anotheris substantially at 45° to the plane of FIG. 16A and is substantiallyorthogonal to the polarization of portions of beams 684A and 684B thatoverlap one another, which is substantially 135° to the plane of FIG.16A. The directions of propagation of beams 682A and 682B are parallel,and the directions of propagation of beams 684A and 684B are parallelbecause the entrance and exit faces of retardation plate 686 aresubstantially parallel.

There is a small lateral displacement S_(b) between beams 682A and 682Band between beams 684A and 684B in FIG. 16A, the two lateraldisplacements being substantially the same. The lateral displacementsare primarily a consequence of the difference in the direction of therespective energy flux vectors and the wave front vectors forextraordinarily polarized beams 682X and 684X in phase retardation plate686. The lateral displacements between beams 682A and 682B and betweenbeams 684A and 684B depicted in FIG. 16A are exaggerated for the purposeof clearly illustrating the effects. Typically, the lateral displacementS_(b) is substantially smaller than the spot size of beam components682A, 682B, 684A, and 684B.

Referring again to FIG. 16A, beams 682A, 682B, 684A, and 684B enter abirefringent prism 688 preferably made of a negative uniaxial crystal,e.g. LiNbO₃, or KDP. The optical axis of birefringent prism 688 is at anangle of 45° to the plane of FIG. 16A. Alternatively, for a birefringentprism 688 made of a positive uniaxial crystal, e.g. quartz or TeO₂, theoptical axis of birefringent prism 688 is orientated at an angle of 135°to the plane of FIG. 16A.

Upon entering birefringent prism 688, each of beams 682A, 682B, 684A,and 684B separate into ordinarily-polarized beams (polarized at about135°) and extraordinarily-polarized beams (polarized at about 45°).Because beams 682A and 682B substantially overlap one another andbecause retardation plate 686 introduces a phase difference betweenthese two beams, the ordinarily polarized beams from beams 682A and 682Bdestructively interfere with one another, substantially canceling outeach other. Thus, the ordinarily polarized beams from 682A and 682B arenot shown in FIG. 16A. Conversely, the extraordinarily polarized beamsfrom beams 682A and 682B constructively interfere with one another andemerge from prism 688 as beams 682C and 682D, respectively, whichsubstantially overlap and have polarizations of 45°. Similarly, theextraordinarily polarized beams from beams 684A and 684B destructivelyinterfere with one another, substantially canceling out each other.Thus, the extraordinarily polarized beams from beams 684A and 684B arenot shown in FIG. 16A. The ordinarily polarized beams from beams 684Aand 684B constructively interfere with one another and emerge from prism688 as beams 684C and 684D, respectively, which substantially overlapand have polarizations of −45°.

The apex angle α₂ of birefringent prism 688 is selected so that beams682C and 682D exit birefringent prism 688 parallel to beams 684C and684D. This is possible because beams 682C and 682D emerge from beamspropagating as extraordinarily polarized beams in prism 688 and beams684C and 684D emerge from beams propagating as ordinarily polarizedbeams in prism 688. As a result, if beams 682 and 684 have substantiallyequal intensities, the system produces a pair of substantiallyequal-intensity output beams, beam 692 (formed from the superposition ofbeams 682C and 682D) and beam 694 (formed from the superposition ofbeams 684C and 684D that propagate parallel to one another and haveorthogonal polarizations (45° and −45°, respectively). There is a smallnon-zero lateral displacement between beams 682D and 684D, S_(a).Typically, this displacement is less than about 100 microns. Beams 682Cand 682D have the same frequency profile as the first input beamcomponent 682 and beams 684C and 684D have the same frequency profile asthe second input beam component 684, which is different from that ofbeams 682C and 682D if, for example, beams 682 and 684 emerge from anacousto-optic modulator within light source 680.

In some cases, such as when the lateral displacement S_(b) is notnegligible, the destructive interference between portions of beams 682Aand 682B that propagate as ordinarily polarized beams within prism 688is not complete. Similarly, the destructive interference betweenportions of beams 684A and 684B that propagate as extraordinarilypolarized beams within prism 688 can also be incomplete. However, evenin these cases, birefringent prism 688 ensures that beam 692 (whichemerges from extraordinarily-polarized beams) has a polarizationorthogonal to the polarization of beam 694 (which emerges fromordinarily-polarized beams). Portions of beams 682A and 682B thatpropagate as ordinarily polarized beams within prism 686 and do notcompletely cancel out because of destructive interference emerge asspurious beams, which diverge away from beams 692 and 694. Similarly,portions of beams 684A and 684B that propagate as extraordinarilypolarized beams within prism 688 and do not completely cancel outbecause of destructive interference emerge as spurious beams, which alsodiverge away from beams 692 and 694. Because of the divergence, aspatial filter can be used to separate the spurious beams from outputbeams 692 and 694.

Many variations of the apparatus shown in FIG. 16A are possible. Forexample, a half-wave plate or quarter-wave plate can be placed betweenphase retarder 686 and birefringent prism 688 such that the output beams694 and 692 are linearly and orthogonally polarized in directions otherthan 45° and −45° in the embodiment discussed above. The optical axis ofbirefringent prism 688 is then oriented at an angle of 90° to plane ofFIG. 16A if the prism is made of a negative uniaxial crystal, or at 0°if the prism is made of positive uniaxial crystal. In anotherembodiment, a Wollaston prism can replace birefringent prism 688 andperform essentially the same function.

In another embodiment for FIG. 16A, a second birefringent prism (notshown) can reduce or substantially eliminate the lateral displacementbetween beams 682D and 684D. In particular, the second birefringentprism causes a compensating lateral displacement that depends on theapex angle of the second birefringent prism, and the apex angle of thesecond birefringent prism can be chosen to eliminate the originaldisplacement.

FIG. 16B illustrates another variant of the embodiment of FIG. 16A,which utilizes a beam source 12R such as described in U.S. Pat. No.6,452,682. Beam source 12R includes two phase retardation plates 754 and758 that are typically made of the same birefringent material. The opticaxis 755 of the phase retardation plate 754 is orientated at an anglewith respect to a normal to the entrance facet of phase retardationplate 754, orthogonal to a normal to the plane of FIG. 16B, and theangle between optical axis 755 of phase retardation plate 754 andoptical axis 759 of phase retardation plate 758 typically is nominally90°. In beam source 12R, a laser system 752 generates an input beam 760having a linear polarization at 45° relative to the optical axis of aretardation plate 754. Upon propagating through retardation plate 754,input beam 760 separates into an extraordinarily-polarized beam 760 aand an ordinarily-polarized beam 760 b. Retardation plate 754 therebyintroduces a lateral displacement or shift between beams 760 a and 760 bas a result of the difference between the directions of the energy fluxvector and the wave front vector for the extraordinarily-polarized beam.

Beams 760 a and 760 b then propagate though an acousto-optic Bragg cell756, which diffracts half of beams 760 a and 760 b intofrequency-shifted beams 760 a 2 and 760 b 2. The undiffracted halves ofbeams 760 a and 760 b emerge from Bragg cell 756 as beams 760 a 1 and760 b 1. Beams 706 a 1, 760 a 2, 760 b 1, and 760 b 2 enter aretardation plate 758. The thickness of phase retardation plate 758 ischosen to exactly compensate for the lateral displacement introduced byphase retardation plate 754. Thus, beams 760 a 1 and 760 b 1 completelyoverlap each other, forming a beam 760-1, and beams 760 a 2 and 762 b 2completely overlap each other forming a beam 760-2 that differs infrequency and polarization from beam 760-1.

A similar method to compensate lateral displacement is shown in FIG. 16Cutilizing another beam source 12S described in U.S. Pat. No. 6,452,682.Beam source 12S is similar to beam source 12R but uses prisms 762 and764, typically non-birefringent, in place of retardation plate 754.Prisms 762 and 764 act as beam expanders in the plane of FIG. 16C beforeBragg cell 756. Similarly, prisms 772 and 774 act as beam contractors inthe plane of FIG. 16C after phase retardation plate 758. The net resultis a reduction in the lateral displacement S_(b) by a factor equal tothe reduction factor of the beam contraction produced by prisms 772 and774, the beam expansion factor of the beam expansion produced by prisms762 and 764 being the reciprocal of the reduction factor of the beamcontraction produced by prisms 772 and 774.

U.S. Pat. No. 6,452,682, which is hereby incorporated by reference inits entirety, further describes light sources using similar techniquesfor generation of suitable heterodyne beams.

Another type of beam source including an AOM uses both diffracted andnon-diffracted beams. FIG. 17A, for example, illustrates a beam source12N including a laser or other light source 702, an acousto-optic Braggcell 704, and an oscillator 706. Beam source 12N converts a singlestabilized frequency, linearly-polarized laser input beam from beamsource 702 into an output beam having two collinearorthogonally-polarized components differing in frequency from each otherby the frequency of a frequency stabilized electrical signal fromelectronic oscillator 706. In operation, oscillator 706 controls a poweramplifier that drives a piezoelectric transducer affixed toacousto-optic Bragg cell 704. Bragg cell 704 is preferably made of auniaxial crystal (e.g., quartz) having an optical axis 705 that makes anangle with the direction of propagation of the acoustic wave 707generated by the piezoelectric transducer. The input beam from laser 702enters Bragg cell 704, becoming an extraordinarily-polarized beam 710traveling at an angle to the optical axis 705 of the crystal in Braggcell 704. Additionally, the photoelastic interaction with the acousticwave under conditions set forth in U.S. Pat. No. 4,687,958, which ishereby incorporated by reference in its entirety, causes Braggdiffraction that generates an ordinarily-polarized beam 708 having ashifted frequency.

Beams 708 and 710 exit acousto-optic Bragg cell 704 through a crystalface on which the piezoelectric transducer is fixed. Under this exitcondition, output beams 708 and 710 are substantially parallel andspatially displaced, typically by only a small fraction of the beamdiameter. Preferably, the electrical output of the power amplifier isadjusted so that exit beams 708 and 710 each have approximately the sameintensity, which is approximately one-half that of input beam.Consequently, the output beam includes the two components 708 and 710,which are collinear, are orthogonally polarized, and differ infrequency.

FIG. 17B shows an example of a beam source 12O containing anacousto-optic Bragg cell 714. Bragg cell 714 is preferably made of auniaxial crystal having an optical axis in the plane of FIG. 17B, whichmakes a first angle with the direction of propagation of an acousticwave 716 generated by piezoelectric transducer 718. The input beamenters Bragg cell 714, becoming an ordinarily-polarized beam that isreflected from surface 714 becoming an ordinarily-polarized beam at asecond angle to the direction of propagation of acoustic wave 716. Dueto the photoelastic interaction of this beam with the acoustic wave 716,Bragg diffraction generates an extraordinarily-polarized beam when therelationships of Equations 3 and 4 are satisfied. In Equations 3 and 4,n_(i) and n_(d) are the indices of refraction for the incident anddiffracted beams, respectively; λ_(o) is the optical wavelength invacuum; v is the acoustic speed; and f_(o) is the drive frequency ofoscillator 706. The angles θ_(i) and θ_(d) are the angles between theincident and diffracted optical beams and the normal to the acousticK-vector, respectively. FIG. 17C illustrates of positive angles θ_(i)and θ_(d).sin θ_(i)=λ_(o)(2n _(i) v){f _(o) +v ²(n _(i) ² −n _(d) ²)/(f _(o)λ_(o)²)}  Equation 3:sin θ_(d)=λ_(o)/(2n _(d) v){f _(o) −v ²(n _(i) ² −n _(d) ²)/(f _(o)λ₀²)}  Equation 4:

Equation 2 above defines the index of refraction n for theextraordinarily polarized beam. The extraordinarily-polarized beampropagates at a small angle relative to the ordinarily-polarized beam,has a polarization orthogonal to that of the ordinarily-polarized beam,and has a frequency shifted by the diffraction from acoustic wave 716. Acrystal face 714B reflects the two orthogonally-polarized beams. Therespective angles of incidence and reflection or refraction for thebeams at crystal faces 714A and 714B can be chosen such that beamsexiting acousto-optic Bragg cell 714 are parallel and spatiallydisplaced by only a small fraction of the beam diameter. For purposes ofillustration, FIG. 17B exaggerates this displacement. Variousmodifications of FIG. 17B can be made to create a different nominalangle (e.g. 180° or 360°) between the input beams and output beams fromthe Bragg cell. It is intended that all combinations of elements andsteps, which perform substantially the same function in substantiallythe same way to achieve the same result, are covered as part of thisembodiment. Other beam paths and angles for the apex faces 714A and 714Bof Bragg cell 714 are further described in U.S. Pat. Nos. 5,862,164 and5,917,844, which are hereby incorporated by reference in its entirety.

FIG. 17D illustrates a beam source 12P such as described in U.S. Pat.No. 5,970,077, which is hereby incorporated by reference in itsentirety. In beam source 12P, a laser or other light source 722 directsan input beam into an acousto-optic crystal setup 840. The plane ofpolarization of beam from laser 722 can be rotated about the beam axisusing techniques known to those skilled in the art, e.g., phaseretardation plates, to form a beam including input beam components 818and 819 having orthogonal linear polarizations. Input beam 818 islinearly polarized perpendicular to the plane of FIG. 17D, and inputbeam 819 is linearly polarized in the plane of FIG. 17D. Both beams 818and 819 have the same frequency f_(L). The relative intensities of beams818 and 819 can be adjusted by control of the degree of rotation appliedto the polarization of the beam from laser 722.

An electrical oscillator 841 preferably provides a frequency stabilizedelectrical signal 842 of frequency f_(o) to a conventional poweramplifier 843. An electrical output signal 844 of power amplifier 843preferably drives a conventional piezoelectric transducer 846 affixed toa crystal 847, which is used to generate an acoustic beam, preferably ofthe shear wave type. Conventional techniques known to those skilled inthe art of acousto-optical modulation are used to absorb in a preferreddistribution the acoustic beam that passes through to the walls ofacousto-optical crystal 847 for the purpose of substantially reducingtemperature gradients in acousto-optical crystal 847. In particular, anabsorber 848 can absorb the acoustic beam at the walls ofacousto-optical crystal 847. The distribution of absorber 848 on thesurface or surfaces of acousto-optical crystal 847 can be designed topermit absorber 848 to make the distribution of energy dissipation ofthe acoustic beam at the walls of acousto-optical crystal 847 correspondto a preferred distribution of absorption of the acoustic beam.

The presently preferred acousto-optical crystal 847 is made of auniaxial crystal having an optical axis 850 that is in the plane of FIG.17D and makes an angle φ with the direction of propagation of theacoustic wave 852 generated by piezoelectric transducer 846. FIG. 17Dillustrates a configuration when acousto-optical crystal 847 contains anegative uniaxial crystal.

Input beam 818 preferably enters acousto-optical crystal 847 at asurface 854 with an angle of incidence φ₁ (as shown in FIG. 17E),becoming an ordinarily polarized beam 820. Beam 820 reflects from asurface 855 becoming an ordinarily polarized beam 822. Beam 822 reflectsfrom a surface 856 becoming ordinarily polarized incident beam 824A.Small angle Bragg diffraction resulting from the photoelasticinteraction of incident beam 824A with the acoustic wave 852 generatesan extraordinarily polarized beam, diffracted beam 824B when Equations 3and 4 above are satisfied. Again, the definitions of angles areillustrated in FIG. 17C, and Equation 2 gives the index of refraction nfor an extraordinarily polarized beam in a birefringent crystal.

Diffracted beam 824B propagates at a small angle to that of thenon-diffracted incident beam 824A, the polarization of diffracted beam824B being orthogonal to that of incident beam 824A. In addition, thefrequency of beam 824B is f_(L)−f₀, while the frequency of beam 824A isf_(L). Beams 824A and 824B reflect from a crystal face 857 becomingbeams 826A and 826B, respectively. Beams 826A and 826B reflect fromcrystal face 858 as beams 828A and 828B, respectively, and beams 828Aand 828B exit acousto-optical crystal 847 at crystal face 859 as beams830A and 830B, respectively.

Input beam 819 preferably enters acousto-optical crystal 847 at surface854 with an angle of incidence φ₁, becoming an extraordinarily polarizedbeam 821. Beam 821 reflects from surface 855 becoming an extraordinarilypolarized beam 823. Beam 823 reflects from surface 856 becomingextraordinarily polarized incident beam 825A. Due to the photoelasticinteraction of incident beam 825A with acoustic wave 852, an ordinarilypolarized, diffracted beam 825B is generated by small angle Braggdiffraction when the relationships given by Equations 3 and 4 aresatisfied.

Diffracted beam 825B propagates at a small angle to that ofnon-diffracted incident beam 825A, the polarization of diffracted beam825B being orthogonal to that of incident beam 825A. In addition, thefrequency of beam 825B is f_(L)+f₀, while the frequency of beam 825A isf_(L). Beams 825A and 825B reflect from crystal face 857 as beams 827Aand 827B, respectively. Beams 827A and 827B reflect from crystal face858 as beams 829A and 829B, respectively, and beams 829A and 829B exitacousto-optical crystal 847 at face 859 as beams 831A and 831B,respectively.

The respective angles of incidence and refraction for beams 818, 819,820, and 821 at surface 854, the respective angles of incidence andreflection for beams 820, 821, 822, and 823 at surface 855, and therespective angles of incidence and reflection for beams 822, 823, 824A,and 825A at surface 856 are chosen such that the angle of deviationbetween beams 824B and 825B is ε−δ where ε is a small angle, preferably0≦ε≦δ, the angle of deviation between beams 824A and 824B is δ, theangle of deviation between beams 825A and 825B is −δ, and the angle ofdeviation between beams 824A and 825A is δ+ε, where δ is specified byEquation 5. In Equation 5, θ is the wavelength of the acoustic beam inacousto-optical crystal 847.sin δ=λ_(o)/(n _(i)Λ)cos θ_(d)=λ_(o)/(n _(d)Λ)cos θ_(i)  Equation 5:

The above condition with respect to relative directions of propagationof beams 824A, 824B, 825A, and 825B can be obtained by choosing the apexangles α₁ and α₂ illustrated in FIG. 17E to satisfy Equation 6. InEquation 6, n′_(1e)=n_(2e) are the indices of refraction for beam 821 atsurfaces 854 and 855, respectively, n′_(2e)=n_(3e) are the indices ofrefraction for beam 823 at surfaces 855 and 856, respectively, andn′_(3e) is the index of refraction for beam 825A at surface 856.δ+ε={α₂−α₁+sin⁻¹(sin φ₁ /n _(o))}−sin⁻¹{(n _(3e) /n′ _(3e))sin{α₂−sin⁻¹{(n _(2e) /n′ _(2e))sin [α₁−sin⁻¹}sin φ₁ /n′_(1e}]]}})  Equation 6:

The respective angles of incidence and reflection for beams 824A, 824B,825A, 825B, 826A, 826B, 827A, and 827B at surface 857, the respectiveangles of incidence and reflection for beams 826A, 826B, 827A, 827B,828A, 828B, 829A, and 829B at surface 858, and the respective angles ofincidence and refraction for beams 828A, 828B, 829A, 829B, 830A, 830B,831A, and 831B at surface 859 are chosen such that beams 830B and 831Bpreferably are parallel. Beams 830B and 831B preferably are spatiallydisplaced by a minute amount, i.e., a small fraction of the beamdiameters, therein being substantially coextensive. The conditions withrespect to the relative directions of propagation of beams 831B and 830Bare obtained by choosing the apex angles satisfying Equation 7. InEquation 7, α₃ and α₄ are angles shown in FIG. 17E, n′_(4e)=n_(5e) arethe indices of refraction for beam 828B at surfaces 859 and 858,respectively, n′_(5e)=n_(6e) are the indices of refraction for beam 826Bat surfaces 858 and 857, respectively, and n′_(6e) is the index ofrefraction for beam 824B at surface 857.δ−ε={α₄−α₃+sin⁻¹(sin φ₂ /n _(o))}−sin⁻¹{(n _(6e) /n′ _(6e))sin{α₄−sin⁻¹{(n _(5e) /n′ _(5e))sin [α₃−sin⁻¹{sin φ₂ /n′_(4e}]]}})  Equation 7:

When it is desired to have the beams 830B and 831B be not parallel,i.e., φ₂ for beam 830B not the same as φ₂ for beam 831B, then the valuesof the parameters of Equations 5 and 6 may be chosen so that beams 830Band 831B have a predetermined angle of divergence or convergence betweenthem. In addition, when it is desired to have beams 818 and 819 be notparallel, i.e., φ₁ for beam 818 not the same as φ₂ for beam 819, thenthe values of parameters of Equations 5 and 6 may also be chosen so thatbeams 818 and 819 have a predetermined angle of divergence orconvergence between them.

Preferably, the electrical output 844 of power amplifier 843 is adjustedso that intensity of principal output beam 830B relative to theintensity of the input beam 818 is some selected nominal value between0% and 100%, preferably 100%. The ratio of the intensity of principaloutput beam 831B to the intensity of beam 819 is substantially the sameas the ratio of the intensity of beam 830B to the intensity of beam 818.Further, beams 830B and 831B are orthogonally polarized andsubstantially coextensive. The frequencies of principal output beams831B and 830B differ by 2f₀ and differ from the frequency of beam 1016by ±f₀, respectively.

Spurious secondary output beams 830A and 831A are orthogonally polarizedbeams with frequencies the same as the frequency of beam 816. Thedirections of propagation of secondary output beams 830A and 831Adeviate from the direction of propagation of principal output beams 830Band 831B by approximately −n_(o)ε and n_(o)ε, respectively. Theintensities of the secondary output beams 830A and 831A preferably havenominal values of 0% of the intensities of principal output beams 830Band 831B, respectively, as a consequence of the adjustment of electricaloutput 844 of the power amplifier 843 so that intensity of eitherprincipal output beam 830B relative to the intensity of input beam 818or principal output beam 831B relative to the intensity of the inputbeam 819 preferably is the nominal value of 100%.

An important feature of the embodiment shown in FIG. 17D is anintrinsically low level of contamination of the output beams withnon-shifted frequency components having directions of propagationsubstantially parallel with the direction of propagation of theprincipal output beams 830B and 831B. The low level of contamination inthe system is a consequence of using non normal Bragg diffraction, Braggdiffraction in an uniaxial crystal, instead of normal Bragg diffractionand the absence of additional optical elements such as those made ofbirefringent crystals that would otherwise be required in the path ofthe output beams to make a pair of output beams parallel. Theorientation of the polarization states of the principal output beamswhen using non-normal Bragg diffraction are determined by a plane and anormal to the plane, the plane being defined by the optical axis of theacousto-optical crystal 847 and the direction of propagation of theincident beams 824A and 825A in acousto-optical crystal 847. In a normalBragg diffraction process, however, the orientation of the polarizationstate of the diffracted component of an output beam is the same as thepolarization state of the progenitor incident beam. This feature of anormal Bragg diffraction process generally leads to a requirement for anadditional birefringent optical element to follow the acousto-opticalapparatus and render, if desired, the components of an output beamparallel. An additional birefringent optical element is a potentialgenerator of output beam contamination, the output beam contaminationarising from a misalignment of the additional birefringent opticalelement with respect to the acousto-optical apparatus.

Alternative embodiments to the system shown in FIG. 17D can includebirefringent prisms used to change the relative directions ofpropagation of orthogonally polarized beams such as used in U.S. Pat.No. 5,970,077. The prisms may be independent components or be affixed tothe Bragg cell or other optical components. Spatial filters may also beplaced at the output to help discriminate against secondary beams.

FIG. 18 illustrates a beam source 12Q such as described in U.S. Pat. No.6,157,660, which is hereby incorporated by reference in its entirety.Beam source 12Q includes a laser or other light source 732 that producesa linearly-polarized monochromatic beam perpendicular to the plane ofthe figure. This beam is directed into an acousto-optic crystal 734. Inthis embodiment, crystal 734 is made of an optically active uniaxialcrystal having an optic axis 746 in the plane of FIG. 18 which makes anangle with a normal to the direction of wave front vector K⁽¹⁾ of thefirst acoustic wave generated by a piezoelectric transducer 748. Theillustration shown in FIG. 18 is for an acousto-optical modulator cellcomprised of a left-handed rotating positive uniaxial crystal, e.g.,paratellurite. A first amplified oscillator 736 drives a firstpiezoelectric transducer affixed to acousto-optic crystal 734, and asecond amplified oscillator 738 drives a second piezoelectric transduceraffixed to acousto-optic crystal 734. The first and second acousticwaves are preferably of the shear wave type. The absorption of acousticbeams at the walls of acousto-optical modulator cell 734 is by absorbers734C and 734D.

Referring to FIG. 18, light beam source 732 generates an input beam 731that enters acousto-optical modulator cell 734, and exits theacousto-optical apparatus as output beams 760 and 762 and the series ofsecondary output beams. Output beams 760 and 762 are substantiallylinearly polarized.

A source of a first subset of the secondary output beams is theelliptically polarized eigenmodes for the propagation of light beams inacousto-optical modulator cell 734 comprising an optically activeanisotropic crystal. The elliptical polarization of the eigenmodes ofacousto-optical modulator cell 734 and the boundary conditions that mustbe satisfied by electric and magnetic fields of light beams beingreflected and refracted at interfaces of optically active anisotropiccrystals generate the first subset of the secondary output beams. Thesesecondary output beams generally have reduced intensities in theapparatus. The first subset of the secondary beams have directions ofpropagation different from the directions of propagation of output beams760 and 762 principally because of properties of birefringent truncatedprisms 740 and 742.

Input beam 731 enters acousto-optical modulator cell 734 and, through anacousto-optical interaction with a first acoustic beam in the firstinteraction region 734A, is converted to an intermediate beam. Theintensity of the intermediate beam is preferably substantially the sameas the intensity of input beam 731. The intermediate beam subsequentlypasses through a second acoustic beam in the second interaction region734B. By way of an acousto-optical interaction of the intermediate beamwith the second acoustic beam, a portion of the intermediate beam isconverted into a beam exiting acousto-optical apparatus as one of theoutput beams 760 and 762 with the remaining non-converted portion of theintermediate beam exiting acousto-optical apparatus as the other of theoutput beams 760 and 762.

Incomplete conversion of input beam 732 into the intermediate beamgenerates a second subset of the secondary output beams. The secondsubset of the secondary beams have reduced intensities in the apparatusand have directions of propagation different from the directions ofpropagation of output beams 760 and 762.

The net relative lateral displacements for beams 760 and 762 one withrespect to the other, the displacements due to different directions ofwave front vectors of internal optical beams in acousto-opticalapparatus shown in FIG. 18 and to deviations of energy flux vectors fromcorresponding wave front vectors for optical beams propagating in abirefringent medium, are compensated for to a high level because of thedesign of compensating truncated prisms 740 and 742 shown in FIG. 18.The optic axes for prisms 740 and 742 are orthogonal to the plane ofFIG. 18. The prisms 740 and 742 may be affixed to the acousto-opticcrystal as shown, or may be used as separate, individual components.

Although the invention has been described with reference to particularembodiments, the description is only an example of the invention'sapplication and should not be taken as a limitation. Various adaptationsand combinations of features of the embodiments disclosed are within thescope of the invention as defined by the following claims.

1. A delivery method for a heterodyne beam comprising: generating afirst beam of light with a first polarization and a first frequency anda second beam of light with a second polarization and a secondfrequency; directing the first beam and the second beam into apolarization state modulator (PSM) that is operable to change thepolarizations of the first beam and the second beam in response to acontrol signal; coupling the first beam and the second beam into anoptical fiber; generating a beat signal from the first beam and thesecond beam after the first beam and the second beam exit from theoptical fiber; and using the beat signal in generation of the controlsignal for the PSM.
 2. The method of claim 1, wherein coupling the firstbeam and the second beam into the optical fiber occurs after the firstbeam and the second beam exit from the PSM.
 3. The method of claim 1,wherein directing the first beam and the second beam into the PSM occursafter the first beam and the second beam exit from the optical fiber. 4.The method of claim 1, wherein generating the beat signal comprisesgenerating the beat signal in a first detector path that receives thefirst beam and the second beam after propagation through the opticalfiber, and wherein the method further comprises: generating a secondbeat signal in a second detector path that receives the first beam andthe second beam after propagation through the optical fiber; generatinga third beat signal in a third detector path that receives the firstbeam and the second beam after propagation through the optical fiber;and generating a phase signal in response to the second and the thirdbeat signals, wherein the controller uses the phase signal whengenerating the control signal.
 5. The method of claim 1, whereingenerating the first beam and the second beam comprises operating alaser.
 6. The method of claim 5, wherein the laser comprises a Zeemansplit-laser.
 7. The method of claim 5, wherein directing the first beamand the second beam into the PSM comprises directing the first beam andthe second beam through a birefringent plate between the laser and thePSM.
 8. The method of claim 5, wherein the laser comprises a resonantcavity containing a birefringent element positioned such that theresonant cavity has a first optical path length for a first polarizationof light and a second optical path length for a second polarization oflight.
 9. The method of claim 5, wherein the laser comprises a masterlaser that produces a first output beam, and generating the first beamand the second beam further comprises: operating a slave laser thatproduces a second output beam having a frequency that is adjustable inresponse to a second control signal; and measuring a frequencydifference between the first output beam and the second output beam; andgenerating the control signal as required to set the second output beamat the frequency that provides a desired frequency difference.
 10. Themethod of claim 5, wherein generating the first beam and the second beamfurther comprises operating an optical element that acts as a rotatinghalf-wave plate through which a beam from the laser passes.
 11. Themethod of claim 10, wherein the optical element comprises anelectro-optic crystal, and operating the optical element comprises:applying a first alternating voltage across the electro-optic crystal ina first direction; and applying a second alternating voltage across theelectro-optic crystal in a second direction.
 12. The method of claim 11,wherein the first polarization of the first beam when entering theelectro-optic crystal is a circular polarization, and the secondpolarization of the second beam when entering the electro-optic crystalis a circular polarization that is orthogonal to the first polarization.13. The method of claim 10, wherein the laser is a Zeeman-split laser.14. The method of claim 5, wherein generating the first beam and thesecond beam further comprises: splitting a beam from the laser with apolarizing beam splitter to produce a first polarization component and asecond polarization component; and directing the first polarizationcomponent through a first acousto-optic modulator.
 15. The method ofclaim 14, wherein generating the first beam and the second beam furthercomprises directing the second polarization component through a secondacousto-optic modulator.
 16. The method of claim 14, wherein thepolarizing beam splitter is selected from a group consisting of abirefringent element and a film that is reflective for one of the firstand second polarization components and transparent for the other of thefirst and second polarization components.
 17. The method of claim 14,wherein the laser is a Zeeman-split laser.
 18. The method of claim 5,wherein generating the first beam and the second beam further comprisesoperating an acousto-optic crystal in a path of an output beam from thelaser, wherein at least one of the first beam and the second beamcomprises light diffracted by an acoustic wave traversing theacousto-optic crystal.
 19. The method of claim 18, wherein one of thefirst beam and the second beam comprises light not diffracted by theacoustic wave traversing the acousto-optic crystal.
 20. The method ofclaim 18, wherein the acoustic wave comprises a first acoustic componentand a second acoustic component, and a difference between the firstfrequency of the first beam and the second frequency of the second beamdepends on a difference between a frequency of the first acousticcomponent and a frequency of the second acoustic component.
 21. Themethod of claim 20, wherein the first acoustic component traverses afirst portion of the acousto-optic crystal, and the second acousticcomponent traverses a second portion of the acousto-optic crystal thatis separated from the first portion of the acousto-optic crystal. 22.The method of claim 18, wherein the acousto-optic crystal has an opticalaxis at a non-zero angle to a direction of propagation of the acousticwave.
 23. The method of claim 18, wherein the acoustic wave traverses aninteraction region in the acousto-optic crystal, and the output beamfrom the laser is internally reflected within the acousto-optic crystalcausing the output beam to traverse an interaction region more thanonce.
 24. The method of claim 18, wherein generating the first beam andthe second beam further comprises: splitting the output beam from thelaser into a first polarization component and a second polarizationcomponent that are both directed into the acousto-optic crystal;combining portions of the first polarization component and the secondpolarization component that were diffracted by the acoustic wave in theacousto-optic crystal; and combining portions of the first polarizationcomponent and the second polarization component that were not diffractedby the acoustic wave in the acousto-optic crystal.
 25. The method ofclaim 24, wherein a birefringent optical element is used to perform atleast one of the splitting and/or combining steps.